#include<bits/stdc++.h>
#include <immintrin.h>
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#define FOR(i,n) for(int i = 0; i < (n); i++)
#define sz(c) ((int)(c).size())
#define ten(x) ((int)1e##x)
#define all(v) (v).begin(), (v).end()
using namespace std;
using ll=long long;
using P = pair<ll,ll>;
const long double PI=acos(-1);
const ll INF=1e18;
const int inf=1e9;
template<int MOD> struct Fp{
  ll val;
  constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
    if (val < 0) val += MOD;
  }
  static constexpr int getmod() { return MOD; }
  constexpr Fp operator - () const noexcept {
    return val ? MOD - val : 0;
  }
  constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
  constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
  constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
  constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
  constexpr Fp& operator += (const Fp& r) noexcept {
    val += r.val;
    if (val >= MOD) val -= MOD;
    return *this;
  }
  constexpr Fp& operator -= (const Fp& r) noexcept {
    val -= r.val;
    if (val < 0) val += MOD;
    return *this;
  }
  constexpr Fp& operator *= (const Fp& r) noexcept {
    val = val * r.val % MOD;
    return *this;
  }
  constexpr Fp& operator /= (const Fp& r) noexcept {
    ll a = r.val, b = MOD, u = 1, v = 0;
    while (b) {
      ll t = a / b;
      a -= t * b, swap(a, b);
      u -= t * v, swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0) val += MOD;
    return *this;
  }
  constexpr bool operator == (const Fp& r) const noexcept {
    return this->val == r.val;
  }
  constexpr bool operator != (const Fp& r) const noexcept {
    return this->val != r.val;
  }
  constexpr bool operator < (const Fp& r) const noexcept {
    return this->val < r.val;
  }
  friend constexpr istream& operator >> (istream& is, Fp<MOD>& x) noexcept {
    is >> x.val;
    x.val %= MOD;
    if (x.val < 0) x.val += MOD;
    return is;
  }
  friend constexpr ostream& operator << (ostream& os, const Fp<MOD>& x) noexcept {
    return os << x.val;
  }
  friend constexpr Fp<MOD> modpow(const Fp<MOD>& a, long long n) noexcept {
    Fp<MOD> res=1,r=a;
    while(n){
      if(n&1) res*=r;
      r*=r;
      n>>=1;
    }
    return res;
  }
  friend constexpr Fp<MOD> modinv(const Fp<MOD>& r) noexcept {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b, swap(a, b);
            u -= t * v, swap(u, v);
        }
        return Fp<MOD>(u);
  }
  ll get(){
      return val;
  }
  explicit operator bool()const{
		return val;
  }
};
template< uint32_t mod, bool fast = false >
struct MontgomeryModInt {
  using mint = MontgomeryModInt;
  using i32 = int32_t;
  using i64 = int64_t;
  using u32 = uint32_t;
  using u64 = uint64_t;
 
  static constexpr u32 get_r() {
    u32 ret = mod;
    for(i32 i = 0; i < 4; i++) ret *= 2 - mod * ret;
    return ret;
  }
 
  static constexpr u32 r = get_r();
  static constexpr u32 n2 = -u64(mod) % mod;
 
  static_assert(r * mod == 1, "invalid, r * mod != 1");
  static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
 
  u32 a;
 
  MontgomeryModInt() : a{} {}
 
  MontgomeryModInt(const i64 &x)
      : a(reduce(u64(fast ? x : (x % mod + mod)) * n2)) {}
 
  static constexpr u32 reduce(const u64 &b) {
    return u32(b >> 32) + mod - u32((u64(u32(b) * r) * mod) >> 32);
  }
 
  constexpr mint& operator+=(const mint &p) {
    if(i32(a += p.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }
 
  constexpr mint& operator-=(const mint &p) {
    if(i32(a -= p.a) < 0) a += 2 * mod;
    return *this;
  }
 
  constexpr mint& operator*=(const mint &p) {
    a = reduce(u64(a) * p.a);
    return *this;
  }
 
  constexpr mint& operator/=(const mint &p) {
    *this *= modinv(p);
    return *this;
  }
 
  constexpr mint operator-() const { return mint() - *this; }
 
  constexpr mint operator+(const mint &p) const { return mint(*this) += p; }
 
  constexpr mint operator-(const mint &p) const { return mint(*this) -= p; }
 
  constexpr mint operator*(const mint &p) const { return mint(*this) *= p; }
 
  constexpr mint operator/(const mint &p) const { return mint(*this) /= p; }
 
  constexpr bool operator==(const mint &p) const { return (a >= mod ? a - mod : a) == (p.a >= mod ? p.a - mod : p.a); }
 
  constexpr bool operator!=(const mint &p) const { return (a >= mod ? a - mod : a) != (p.a >= mod ? p.a - mod : p.a); }
 
  u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }
 
  friend constexpr MontgomeryModInt<mod> modpow(const MontgomeryModInt<mod> &x,u64 n) noexcept {
    MontgomeryModInt<mod> ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
 
  friend constexpr MontgomeryModInt<mod> modinv(const MontgomeryModInt<mod> &r) noexcept {
        u64 a = r.get(), b = mod, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b, swap(a, b);
            u -= t * v, swap(u, v);
        }
        return MontgomeryModInt<mod>(u);
  }
 
  friend ostream &operator<<(ostream &os, const mint &p) {
    return os << p.get();
  }
 
  friend istream &operator>>(istream &is, mint &a) {
    i64 t;
    is >> t;
    a = mint(t);
    return is;
  }
  static constexpr u32 getmod() { return mod; }
};
ll mod(ll a,ll MOD){
    if(a<0) a+=MOD;
    return a%MOD;
}
ll modpow(ll a,ll n,ll mod){
  ll res=1;
  a%=mod;
  while (n>0){
    if (n & 1) res*=a;
    a *= a;
    a%=mod;
    n >>= 1;
    res%=mod;
  }
  return res;
}
vector<P> prime_factorize(ll N) {
  vector<P> res;
  for (ll a = 2; a * a <= N; ++a) {
    if (N % a != 0) continue;
    ll ex = 0;
    while(N % a == 0){
      ++ex;
      N /= a;
    }
    res.push_back({a, ex});
  }
  if (N != 1) res.push_back({N, 1});
  return res;
}
ll modinv(ll a, ll mod) {
    ll b = mod, u = 1, v = 0;
    while (b) {
        ll t = a/b;
        a -= t * b, swap(a, b);
        u -= t * v, swap(u, v);
    }
    u %= mod;
    if (u < 0) u += mod;
    return u;
}
ll extGcd(ll a, ll b, ll &p, ll &q) {  
    if (b == 0) { p = 1; q = 0; return a; }  
    ll d = extGcd(b, a%b, q, p);  
    q -= a/b * p;  
    return d;  
}
P ChineseRem(const vector<ll> &b, const vector<ll> &m) {
  ll r = 0, M = 1;
  for (int i = 0; i < (int)b.size(); ++i) {
    ll p, q;
    ll d = extGcd(M, m[i], p, q);
    if ((b[i] - r) % d != 0) return make_pair(0, -1);
    ll tmp = (b[i] - r) / d * p % (m[i]/d);
    r += M * tmp;
    M *= m[i]/d;
  }
  return make_pair(mod(r, M), M);
}
//fast Input by yosupo
#include <unistd.h>
#include <algorithm>
#include <array>
#include <cassert>
#include <cctype>
#include <cstring>
#include <sstream>
#include <string>
#include <type_traits>
#include <vector>
namespace fastio{
/*
  quote from yosupo's submission in Library Checker
*/
int bsr(unsigned int n) {
    return 8 * (int)sizeof(unsigned int) - 1 - __builtin_clz(n);
}
// @param n `1 <= n`
// @return maximum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsr(unsigned long n) {
    return 8 * (int)sizeof(unsigned long) - 1 - __builtin_clzl(n);
}
// @param n `1 <= n`
// @return maximum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsr(unsigned long long n) {
    return 8 * (int)sizeof(unsigned long long) - 1 - __builtin_clzll(n);
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsr(unsigned __int128 n) {
    unsigned long long low = (unsigned long long)(n);
    unsigned long long high = (unsigned long long)(n >> 64);
    return high ? 127 - __builtin_clzll(high) : 63 - __builtin_ctzll(low);
}
 
namespace internal {
 
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;
 
template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;
 
template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;
 
template <class T>
using is_integral =
    typename std::conditional<std::is_integral<T>::value ||
                                  internal::is_signed_int128<T>::value ||
                                  internal::is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;
 
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;
 
template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;
 
template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;
 
template <class T>
using is_integral_t = std::enable_if_t<is_integral<T>::value>;
 
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
 
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
 
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
 
}  // namespace internal
struct Scanner {
  public:
    Scanner(const Scanner&) = delete;
    Scanner& operator=(const Scanner&) = delete;
 
    Scanner(FILE* fp) : fd(fileno(fp)) {}
 
    void read() {}
    template <class H, class... T> void read(H& h, T&... t) {
        bool f = read_single(h);
        assert(f);
        read(t...);
    }
 
    int read_unsafe() { return 0; }
    template <class H, class... T> int read_unsafe(H& h, T&... t) {
        bool f = read_single(h);
        if (!f) return 0;
        return 1 + read_unsafe(t...);
    }
 
    int close() { return ::close(fd); }
 
  private:
    static constexpr int SIZE = 1 << 15;
 
    int fd = -1;
    std::array<char, SIZE + 1> line;
    int st = 0, ed = 0;
    bool eof = false;
 
    bool read_single(std::string& ref) {
        if (!skip_space()) return false;
        ref = "";
        while (true) {
            char c = top();
            if (c <= ' ') break;
            ref += c;
            st++;
        }
        return true;
    }
    bool read_single(double& ref) {
        std::string s;
        if (!read_single(s)) return false;
        ref = std::stod(s);
        return true;
    }
 
    template <class T,
              std::enable_if_t<std::is_same<T, char>::value>* = nullptr>
    bool read_single(T& ref) {
        if (!skip_space<50>()) return false;
        ref = top();
        st++;
        return true;
    }
 
    template <class T,
              internal::is_signed_int_t<T>* = nullptr,
              std::enable_if_t<!std::is_same<T, char>::value>* = nullptr>
    bool read_single(T& sref) {
        using U = internal::to_unsigned_t<T>;
        if (!skip_space<50>()) return false;
        bool neg = false;
        if (line[st] == '-') {
            neg = true;
            st++;
        }
        U ref = 0;
        do {
            ref = 10 * ref + (line[st++] & 0x0f);
        } while (line[st] >= '0');
        sref = neg ? -ref : ref;
        return true;
    }
    template <class U,
              internal::is_unsigned_int_t<U>* = nullptr,
              std::enable_if_t<!std::is_same<U, char>::value>* = nullptr>
    bool read_single(U& ref) {
        if (!skip_space<50>()) return false;
        ref = 0;
        do {
            ref = 10 * ref + (line[st++] & 0x0f);
        } while (line[st] >= '0');
        return true;
    }
 
    bool reread() {
        if (ed - st >= 50) return true;
        if (st > SIZE / 2) {
            std::memmove(line.data(), line.data() + st, ed - st);
            ed -= st;
            st = 0;
        }
        if (eof) return false;
        auto u = ::read(fd, line.data() + ed, SIZE - ed);
        if (u == 0) {
            eof = true;
            line[ed] = '\0';
            u = 1;
        }
        ed += int(u);
        line[ed] = char(127);
        return true;
    }
 
    char top() {
        if (st == ed) {
            bool f = reread();
            assert(f);
        }
        return line[st];
    }
 
    template <int TOKEN_LEN = 0>
    bool skip_space() {
        while (true) {
            while (line[st] <= ' ') st++;   
            if (ed - st > TOKEN_LEN) return true;
            if (st > ed) st = ed;
            for (auto i = st; i < ed; i++) {
                if (line[i] <= ' ') return true;
            }
            if (!reread()) return false;
        }
    }
};

//fast Output by ei1333
/**
 * @brief Printer(高速出力)
 */
struct Printer {
public:
  explicit Printer(FILE *fp) : fp(fp) {}

  ~Printer() { flush(); }

  template< bool f = false, typename T, typename... E >
  void write(const T &t, const E &... e) {
    if(f) write_single(' ');
    write_single(t);
    write< true >(e...);
  }

  template< typename... T >
  void writeln(const T &...t) {
    write(t...);
    write_single('\n');
  }

  void flush() {
    fwrite(line, 1, st - line, fp);
    st = line;
  }

private:
  FILE *fp = nullptr;
  static constexpr size_t line_size = 1 << 16;
  static constexpr size_t int_digits = 20;
  char line[line_size + 1] = {};
  char small[32] = {};
  char *st = line;

  template< bool f = false >
  void write() {}

  void write_single(const char &t) {
    if(st + 1 >= line + line_size) flush();
    *st++ = t;
  }

  template< typename T, enable_if_t< is_integral< T >::value, int > = 0 >
  void write_single(T s) {
    if(st + int_digits >= line + line_size) flush();
    if(s == 0) {
      write_single('0');
      return;
    }
    if(s < 0) {
      write_single('-');
      s = -s;
    }
    char *mp = small + sizeof(small);
    typename make_unsigned< T >::type y = s;
    size_t len = 0;
    while(y > 0) {
      *--mp = y % 10 + '0';
      y /= 10;
      ++len;
    }
    memmove(st, mp, len);
    st += len;
  }

  void write_single(const string &s) {
    for(auto &c : s) write_single(c);
  }

  void write_single(const char *s) {
    while(*s != 0) write_single(*s++);
  }

  template< typename T >
  void write_single(const vector< T > &s) {
    for(size_t i = 0; i < s.size(); i++) {
      if(i) write_single(' ');
      write_single(s[i]);
    }
  }
};

}; //namespace fastio
using mint=MontgomeryModInt<998244353>;
int main(){
    fastio::Scanner sc(stdin);
    fastio::Printer pr(stdout);
    #define in(...) sc.read(__VA_ARGS__)
    #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
    #define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
    #define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
    #define out(...) pr.write(__VA_ARGS__)
    #define outln(...) pr.writeln(__VA_ARGS__)
    #define outspace(...) pr.write(__VA_ARGS__),pr.write(' ')
    #define rall(v) (v).rbegin(), (v).rend()
    #define fi first
    #define se second
    /*
        ここでは左上を(0,0)として考える
        以下のパターン
        ①上下、左右 2^H+2^W
        ②x+yが偶数に上下x+yが奇数に左右、その逆、同じ行、列には左右、上下はない。2*2^H*2^W
        ③上左、右下はx+y mod gでそれぞれ決まる、2*2^g
        ④上右、左下はx-y mod g 2*2^g
        1,3,4はいかなるgについても存在する
        2はgが偶数の時のみ(奇数の時はx+y≡2 mod gとx+y≡0 mod 2が同値でない)
        1,3,4で重複が8(4方向*2)
        1,2,3,4で重複が16(1,3,4の8+2*(2の縦横それぞれ1方向のケース(=4)))
        これ以外のケースを考える
        1,2,3,4を満たしていない数え上げたい対象は4*4グリッドの周期になる
        (証明は解説に任せる(え？))
        当然、ここまでくればグリッドを全探索すれば良い
        (このグリッドには2ヶ所同じ方向があって、探索するのは4^8通り)
        全体のグリッドがトーラスであることを考えると、ちゃんと4*4のグリッドでピッタリ敷き詰められる必要があり
        gが4の倍数の時しかこのケースは存在しない
        このケースのうち1,2,3,4と被らないものは48通り存在する。(全探索)
        K>0の時
        すでに書き込まれた数によって固定されるものを考えれば良い、実装はとてつもなく大変
        コメント:
        割り当てる方向の個数が3つ以上の数え上げは、②を計算することにより残るものが
        定数個になるというの、とても難しかった、めっちゃadhoc
        どうやって作問したんですか？
    */
    auto calc=[](map<int,char> &mp){
        map<char,int> d;
        for(auto& [key,val]:mp) d[val]++;
        int ret=0;
        for(auto& [c,cnt]:d) if(cnt>0) ret++;
        return ret;
    };
    INT(t);
    assert(1<=t&&t<=100);
    while(t--){
        LL(h,w,k);
        assert(1<=h&&h<=1000000000&&1<=w&&w<=1000000000&&0<=k&&k<=min(2000ll,h*w));
        ll g=gcd(h,w);
        mint ans=0;
        if(k==0){
            if(g%4==0){
                ans=modpow(mint(2),h)+modpow(mint(2),w)+modpow(mint(2),h+w+1)+modpow(mint(2),g)*4+32;
            }else if(g%4==2){
                ans=modpow(mint(2),h)+modpow(mint(2),w)+modpow(mint(2),h+w+1)+modpow(mint(2),g)*4-16;
            }else{
                ans=modpow(mint(2),h)+modpow(mint(2),w)+modpow(mint(2),g)*4-8;
            }
            outln(ans.get());
            continue;
        }
        swap(h,w);
        vector<ll> x(k),y(k);
        vector<char> d(k);
        bool hasver=false,hashor=false;
        FOR(i,k){
            in(y[i],x[i],d[i]);
            y[i]=w-y[i]-1;
            x[i]=h-x[i]-1;
            assert(0<=x[i]&&x[i]<h&&0<=y[i]&&y[i]<w);
            assert(d[i]=='R'||d[i]=='L'||d[i]=='U'||d[i]=='D');
            if(d[i]=='L'||d[i]=='R') hashor=true;
            else hasver=true;
        }
        //case 1
        if(!hasver||!hashor){
            map<int,vector<char>> X,Y;
            FOR(i,k){
                X[x[i]].push_back(d[i]);
                Y[y[i]].push_back(d[i]);
            }
            bool ret0h=false,ret0w=false;
            ll h1=h,w1=w;
            for(auto& [key,val]:X){
                sort(all(val));
                val.erase(unique(all(val)),val.end());
                if(val.size()>1) ret0h=true;
                for(auto& element:val){
                    if(element!='L'&&element!='R') ret0h=true;
                }
                if(ret0h) break;
                h1--;
            }
            for(auto& [key,val]:Y){
                sort(all(val));
                val.erase(unique(all(val)),val.end());
                if(val.size()>1) ret0w=true;
                for(auto& element:val){
                    if(element!='U'&&element!='D') ret0w=true;
                }
                if(ret0w) break;
                w1--;
            }
            if(!ret0h) ans+=modpow(mint(2),h1);
            if(!ret0w) ans+=modpow(mint(2),w1);
        }
        //case 2
        if(g%2==0){
            bool oddver=false,oddhor=false,evenver=false,evenhor=false;
            FOR(i,k){
                if((x[i]+y[i])%2){
                    if(d[i]=='L'||d[i]=='R') oddhor=true;
                    else oddver=true;
                }else{
                    if(d[i]=='L'||d[i]=='R') evenhor=true;
                    else evenver=true;
                }
            }
            if(!(oddver&&oddhor)&&!(evenver&&evenhor)&&!(oddver&&evenver)&&!(oddhor&&evenhor)){
                if(evenver||oddhor){
                    bool ret0=false;
                    map<int,char> X,Y;
                    FOR(i,k){
                        if((x[i]+y[i])%2){
                            if(X.find(x[i])==X.end()){
                                X[x[i]]=d[i];
                            }else if(X[x[i]]!=d[i]){
                                ret0=true;
                            }
                        }else{
                            if(Y.find(y[i])==Y.end()){
                                Y[y[i]]=d[i];
                            }else if(Y[y[i]]!=d[i]){
                                ret0=true;
                            }
                        }
                    }
                    if(!ret0){
                        ans+=modpow(mint(2),h+w-X.size()-Y.size())-(2-calc(X))*(2-calc(Y));
                    }
                }
                if(evenhor||oddver){
                    bool ret0=false;
                    map<int,char> X,Y;
                    FOR(i,k){
                        if((x[i]+y[i])%2==0){
                            if(X.find(x[i])==X.end()){
                                X[x[i]]=d[i];
                            }else if(X[x[i]]!=d[i]){
                                ret0=true;
                            }
                        }else{
                            if(Y.find(y[i])==Y.end()){
                                Y[y[i]]=d[i];
                            }else if(Y[y[i]]!=d[i]){
                                ret0=true;
                            }
                        }
                    }
                    if(!ret0){
                        ans+=modpow(mint(2),h+w-X.size()-Y.size())-(2-calc(X))*(2-calc(Y));
                    }
                }
            }
        }
        //case 3
        {
            bool ret0=false;
            map<int,char> mp;
            map<char,int> dc;
            FOR(i,k){
                if(mp.find((x[i]+y[i])%g)==mp.end()){
                    mp[(x[i]+y[i])%g]=d[i];
                }else if(mp[(x[i]+y[i])%g]!=d[i]){
                    ret0=true;
                }
                dc[d[i]]++;
            }
            if((dc['L']>0||dc['U']>0)&&dc['R']==0&&dc['D']==0&&!ret0){
                ans+=modpow(mint(2),g-mp.size())-2+dc.size();
            }else if((dc['R']>0||dc['D']>0)&&dc['L']==0&&dc['U']==0&&!ret0){
                ans+=modpow(mint(2),g-mp.size())-2+dc.size();
            }
        }
        //case 4
        {
            bool ret0=false;
            map<int,char> mp;
            map<char,int> dc;
            FOR(i,k){
                if(mp.find((x[i]+(g-1)*y[i])%g)==mp.end()){
                    mp[(x[i]+(g-1)*y[i])%g]=d[i];
                }else if(mp[(x[i]+(g-1)*y[i])%g]!=d[i]){
                    ret0=true;
                }
                dc[d[i]]++;
            }
            if((dc['L']>0||dc['U']>0)&&dc['R']==0&&dc['D']==0&&!ret0){
                ans+=modpow(mint(2),g-mp.size())-2+dc.size();
            }else if((dc['R']>0||dc['D']>0)&&dc['L']==0&&dc['U']==0&&!ret0){
                ans+=modpow(mint(2),g-mp.size())-2+dc.size();
            }
        }
        //case muzui
        if(g%4==0){
            vector<vector<char>> grid(4,vector<char>(4,'.'));
            bool ret0=false;
            FOR(i,k){
                if(grid[x[i]%4][y[i]%4]=='.'){
                    grid[x[i]%4][y[i]%4]=d[i];
                }else if(grid[x[i]%4][y[i]%4]!=d[i]){
                    ret0=true;
                }
            }
            FOR(i,4) FOR(j,2){
                if(grid[i][j]!='.'&&grid[(i+2)%4][(j+2)%4]!='.'){
                    if(grid[i][j]!=grid[(i+2)%4][(j+2)%4]) ret0=true;
                }else if(grid[i][j]!='.'){
                    grid[(i+2)%4][(j+2)%4]=grid[i][j];
                }else if(grid[(i+2)%4][(j+2)%4]!='.'){
                    grid[i][j]=grid[(i+2)%4][(j+2)%4];
                }
            }
            if(!ret0){
                //すでに1,2,3,4との被りを省いた48通りのうちマッチするものを探し出す
                //このコードを書いてる人は今書いてる時点ですでに疲れており、48通りのグリッドを書き出したくない
                //書き出すグリッドの個数は6個に絞ることができる(トーラス上で8通りのずらす方法がそれぞれある)
                vector<vector<vector<char>>> solution={
                    {
                        {'R','L','R','U'},
                        {'R','L','D','L'},
                        {'R','U','R','L'},
                        {'D','L','R','L'}
                    },
                    {
                        {'L','U','L','R'},
                        {'L','R','D','R'},
                        {'L','R','L','U'},
                        {'D','R','L','R'}
                    },
                    {
                        {'U','U','U','R'},
                        {'L','D','D','D'},
                        {'U','R','U','U'},
                        {'D','D','L','D'}
                    },
                    {
                        {'U','U','U','L'},
                        {'D','D','R','D'},
                        {'U','L','U','U'},
                        {'R','D','D','D'}
                    },
                    {
                        {'U','U','L','R'},
                        {'L','R','D','D'},
                        {'L','R','U','U'},
                        {'D','D','L','R'}
                    },
                    {
                        {'L','U','U','R'},
                        {'L','D','D','R'},
                        {'U','R','L','U'},
                        {'D','R','L','D'}
                    }
                };
                FOR(i,6) FOR(a,4) FOR(b,2){
                    auto& s=solution[i];
                    bool ok=true;
                    FOR(x,4) FOR(y,4){
                        if(grid[x][y]!='.'&&grid[x][y]!=s[(x+a)%4][(y+b)%4]) ok=false;
                    }
                    if(ok) ans+=1;
                }
            }
        }
        outln(ans.get());
    }
}